Fungrim entry: 12b1d0

R_D\!\left(-x, -y, z\right) = -\overline{i R_D\!\left(x, y, -z\right)}

Assumptions:

x \in \left(0, \infty\right] \;\mathbin{\operatorname{and}}\; y \in \left(0, \infty\right] \;\mathbin{\operatorname{and}}\; z \in \left(0, \infty\right]

TeX:

R_D\!\left(-x, -y, z\right) = -\overline{i R_D\!\left(x, y, -z\right)}

x \in \left(0, \infty\right] \;\mathbin{\operatorname{and}}\; y \in \left(0, \infty\right] \;\mathbin{\operatorname{and}}\; z \in \left(0, \infty\right]

Definitions:

Fungrim symbol	Notation	Short description
`CarlsonRD`	$R_D\!\left(x, y, z\right)$	Degenerate Carlson symmetric elliptic integral of the third kind
`Conjugate`	$\overline{z}$	Complex conjugate
`ConstI`	$i$	Imaginary unit
`OpenClosedInterval`	$\left(a, b\right]$	Open-closed interval
`Infinity`	$\infty$	Positive infinity

Source code for this entry:

Entry(ID("12b1d0"),
    Formula(Equal(CarlsonRD(Neg(x), Neg(y), z), Neg(Conjugate(Mul(ConstI, CarlsonRD(x, y, Neg(z))))))),
    Variables(x, y, z),
    Assumptions(And(Element(x, OpenClosedInterval(0, Infinity)), Element(y, OpenClosedInterval(0, Infinity)), Element(z, OpenClosedInterval(0, Infinity)))))

Topics using this entry

Specific values of Carlson symmetric elliptic integrals